The concept of co-operation between the nodes of a wireless network has become increasingly successful over the last few years. It has been shown that certain practical embodiments of this concept make it possible to increase both the spectral efficiencies and the reliability of transmission for wireless communications systems.
Network coding is an advanced form of co-operation in which the nodes of the network share not only their own resources (power, bandwidth, etc.) but also their computation capacities, thereby creating a kind of distributed coding that becomes increasingly powerful as the information propagates through the nodes. This coding leads to substantial gains in terms of diversity and of coding.
In the realistic circumstance of a relay channel having Rayleigh fading with the source having no knowledge of the S→R channel, there exists non-zero probability that the relay will decode the message from the source imperfectly. This can lead to errors being propagated to the destination.
In the prior art, the scientific publication “Joint channel and network decoding for XOR-based relay in multi-access channel” by S. Tang, J. Cheng, C. Sun, R. Miura, S. Obana, published in IEICE Transactions on Communication, Vol. E92-B, No. 11, November 2009, there is disclosed a joint channel/network code for a two-source MARC network that can achieve full diversity, and that takes into consideration the non-reliability of the source-to-relay links by applying the “joint selective” function for relaying. To do this, the relay transmits a network coded version of the messages received if both messages received from the sources are decoded without error. The technique described in that prior art scientific publication includes at least the following two drawbacks:                the relaying function relies on the “joint selective” approach: the relay transmits nothing if one of the two source messages is detected as being erroneous at the relay; and        the “code design” is limited to circumstances in which the sources and the relay use the same coding schemes.        
The scientific publication “Multiple-access relay channel with network coding and non-ideal source-relay channels” by Dereje H. Woldegebreal et al., published in ISWCS 2007, 4th International Symposium on Wireless Communication Systems, 2007, IEEE, Piscataway, N.J., USA, Oct. 1, 2007 pp. 732-736, XP031166866 describes a MARC system in theoretical manner that relies on the assumption that the channel decoding of the signals coming from the sources and the relays is performed separately from the XOR decoding at the destination.
In an “adaptive” mode, the relay transmits network coding only if both of the messages it receives from the sources have been decoded correctly. If this does not happen (an error is detected), either the relay transmits the message that was decoded without error, if there is one, or else the relay remains silent. Error detection may be based on a cyclic redundancy check (CRC) and the relay may then add the transmission of “extra-bits” to indicate the result of the decoding. The publication is concerned essentially with calculating the theoretical performance limits of the MARC system without describing a method of implementing it.